Automatic Block-Length Selection for the Dependent Bootstrap |
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Authors: | Dimitris N. Politis Halbert White |
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Affiliation: | a Department of Mathematics, University of California, San Diego La Jolla, California, USAb Department of Mathematics, University of California, San Diego La Jolla, CA, USAc Department of Economics, University of California, San Diego La Jolla, California, USA |
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Abstract: | We review the different block bootstrap methods for time series, and present them in a unified framework. We then revisit a recent result of Lahiri [Lahiri, S. N. (1999b). Theoretical comparisons of block bootstrap methods, Ann. Statist. 27:386-404] comparing the different methods and give a corrected bound on their asymptotic relative efficiency; we also introduce a new notion of finite-sample “attainable” relative efficiency. Finally, based on the notion of spectral estimation via the flat-top lag-windows of Politis and Romano [Politis, D. N., Romano, J. P. (1995). Bias-corrected nonparametric spectral estimation. J. Time Series Anal. 16:67-103], we propose practically useful estimators of the optimal block size for the aforementioned block bootstrap methods. Our estimators are characterized by the fastest possible rate of convergence which is adaptive on the strength of the correlation of the time series as measured by the correlogram. |
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Keywords: | Bandwidth choice Block bootstrap Resampling Subsampling Time series Variance estimation |
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